the second number is six more than thrice the first number. Twice the first plus the second is 46 .
Answers
Answer:
The sum of three numbers is 16."
x + y + z = 16
:
" The sum of twice the first number, 3 times the second number, and 4 times the third number is 46."
2x = 3y + 4z = 46
:
" The difference between 5 times the first number and the second number is 31."
5x - y = 31
-y = 31 - 5x
y = 5x - 31; multiplied by -1
:
Find the three numbers.
:
Replace y with (5x-31) in the 1st and 2nd equation
x + (5x-31) + z = 16
6x + z = 16 + 31
6x + z = 47
:
2x = 3(5x-31) + 4z = 46
2x = 15x - 93 + 4z = 46
17x + 4z = 46 + 93
17x + 4z = 139
;
Multiply the 1st 2 unknown equation by 4, subtract the 2nd
24x + 4z = 188
17x + 4z = 139
----------------subtraction eliminates z
7x = 49
x = 49%2F7
x = 7
:
Find z using 6x + z = 47
6(7) + z = 47
42 + z = 47
z = 47 - 42
z = 5
;
Use y = 5x - 31 to find y
y = 5(7) - 31
y = 35 - 31
y = 4
SOLUTION
GIVEN
The second number is six more than thrice the first number.
Twice the first plus the second is 46
TO DETERMINE
The numbers
EVALUATION
Let first number = x
Now the second number is six more than thrice the first number.
So second number = 3x + 6
Since Twice the first plus the second is 46
So by the given condition
2x + 3x + 6 = 46
⇒ 5x = 46 - 6
⇒ 5x = 40
⇒ x = 8
Hence we have
First number = 8
Second number = 30
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